In [1]}, the authors show that the problem of determining if \(\operatorname{wcol}_r(G)\le k\)  is NP-hard for \(r\ge 3\) .
Below, we show that in the case when \(r=2\) , it remains NP-hard.
Moreover, we show that determining \(\operatorname{col}_r(G) \le k\)  is also NP-hard for \(r\ge 2\) .
